Given two measured spaces $(X,\mu )$ and $(Y,\nu )$, and a third space $Z$, given two functions $u(x,z)$ and $v(x,z)$, we study the problem of finding two maps $s:X\to Z$ and $t:Y\to Z$ such that the images $s\left(\mu \right)$ and $t\left(\nu \right)$ coincide, and the integral ${\int }_{X}u(x,s\left(x\right))d\mu -{\int }_{Y}v(y,t\left(y\right))d\nu$ is maximal. We give condition on $u$ and $v$ for which there is a unique solution.

Given two measured spaces $(X,\mu )$ and $(Y,\nu )$, and a third space Z, given two functions u(x,z) and v(x,z), we study the problem of finding two maps $s:X\to Z$ and $t:Y\to Z$ such that the images $s\left(\mu \right)$ and $t\left(\nu \right)$ coincide, and the integral ${\int }_{X}u(x,s\left(x\right))d\mu -{\int }_{Y}v(y,t\left(y\right))d\nu$ is maximal. We give condition on u and v for which there is a unique solution.

In this paper we consider hemivariational inequalities of hyperbolic type. The existence result for hemivariational inequality is given and the existence theorem for the optimal shape design problem is shown.

This work concerns controlled Markov chains with finite state space and compact action sets. The decision maker is risk-averse with constant risk-sensitivity, and the performance of a control policy is measured by the long-run average cost criterion. Under standard continuity-compactness conditions, it is shown that the (possibly non-constant) optimal value function is characterized by a system of optimality equations which allows to obtain an optimal stationary policy. Also, it is shown that the...

In this paper, we are interested in finding the optimal shape of a magnet. The criterion to maximize is the jump of the electromagnetic field between two different configurations. We prove existence of an optimal shape into a natural class of domains. We introduce a quasi-Newton type algorithm which moves the boundary. This method is very efficient to improve an initial shape. We give some numerical results.

In this paper, we are interested in finding the optimal shape of a magnet. The criterion to maximize is the jump of the electromagnetic field between two different configurations. We prove existence of an optimal shape into a natural class of domains. We introduce a quasi-Newton type algorithm which moves the boundary. This method is very efficient to improve an initial shape. We give some numerical results.

We propose new alternative theorems for convex infinite systems which constitute the generalization of the corresponding to Gale, Farkas, Gordan and Motzkin. By means of these powerful results we establish new approaches to the Theory of Infinite Linear Inequality Systems, Perfect Duality, Semi-infinite Games and Optimality Theory for non-differentiable convex Semi-Infinite Programming Problem.

We propose an SQP algorithm for mathematical programs with complementarity constraints which solves at each iteration a quadratic program with linear complementarity constraints. We demonstrate how strongly M-stationary solutions of this quadratic program can be obtained by an active set method without using enumeration techniques. We show that all limit points of the sequence of iterates generated by our SQP method are at least M-stationary.

In this paper, a sequential quadratic programming method combined with a trust region globalization strategy is analyzed and studied for solving a certain nonlinear constrained optimization problem with matrix variables. The optimization problem is derived from the infinite-horizon linear quadratic control problem for discrete-time systems when a complete set of state variables is not available. Moreover, a parametrization approach is introduced that does not require starting a feasible solution...

Soit $X$ un espace de Banach de dual topologique $X^{\text{'}}$. $𝒞\left(X\right)$ (resp. $𝒞\left(X^{\text{'}}\right)$) désigne l’ensemble des parties non vides convexes fermées de $X$ (resp. $w^{*}$-fermées de $X^{\text{'}}$) muni de la topologie de la convergence uniforme sur les bornés des fonctions distances. Cette topologie se réduit à celle de la métrique de Hausdorff sur les convexes fermés bornés [16] et admet en général une représentation en terme de cette dernière [11]. De plus, la métrique qui lui est associée s’est révélée très adéquate pour l’étude quantitative...

Let X be a Banach space and X' its continuous dual. C(X) (resp. C(X')) denotes the set of nonempty convex closed subsets of X (resp. ω*-closed subsets of X') endowed with the topology of uniform convergence of distance functions on bounded sets. This topology reduces to the Hausdorff metric topology on the closed and bounded convex sets [16] and in general has a Hausdorff-like presentation [11]. Moreover, this topology is well suited for estimations and constructive approximations [6-9]. We...

Dans cet article, nous étudions la sensibilité d’un problème de contrôle optimal de type bilinéaire. Le coût est différentiable, quadratique et strictement convexe. Le système est gouverné par un opérateur parabolique du quatrième ordre et présente une perturbation additive dans l’équation d’état, ainsi qu’une partie bilinéaire, relativement au contrôle $u$ et à l’état $z$, de la forme $(u·\nabla )z$. Sous des conditions de petitesse de l’état initial et de la perturbation, nous exploitons les propriétés de régularité...